Question

show that $open square brackets table row 1 2 3 row 0 1 0 row 1 1 0 end table close square brackets space open square brackets table row cell negative 1 end cell 1 0 row 0 cell negative 1 end cell 1 row 2 3 4 end table close square brackets not equal to open square brackets table row cell negative 1 end cell 1 0 row 0 cell negative 1 end cell 1 row 2 3 4 end table close square brackets space open square brackets table row 1 2 3 row 0 1 0 row 1 1 0 end table close square brackets$

Solution

open square brackets table row 1 2 3 row 0 1 0 row 1 1 0 end table close square brackets space open square brackets table row cell negative 1 end cell 1 0 row 0 cell negative 1 end cell 1 row 2 3 4 end table close square brackets equals open square brackets table row cell negative 1 plus 0 plus 6 end cell cell 1 minus 2 plus 9 end cell cell 0 plus 2 plus 12 end cell row cell 0 plus 0 plus 0 end cell cell 0 minus 1 plus 0 end cell cell 0 plus 1 plus 0 end cell row cell negative 1 plus 0 plus 0 end cell cell 1 minus 1 plus 0 end cell cell 0 plus 1 plus 0 end cell end table close square brackets equals open square brackets table row 5 8 14 row 0 cell negative 1 end cell 1 row cell negative 1 end cell 0 1 end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis therefore space open square brackets table row 1 2 3 row 0 1 0 row 1 1 0 end table close square brackets space open square brackets table row cell negative 1 end cell 1 0 row 0 cell negative 1 end cell 1 row 2 3 4 end table close square brackets space equals space open square brackets table row 5 8 14 row 0 cell negative 1 end cell 1 row cell negative 1 end cell 0 1 end table close square brackets Also space space space open square brackets table row cell negative 1 end cell 1 0 row 0 cell negative 1 end cell 1 row 2 3 4 end table close square brackets space open square brackets table row 1 2 3 row 0 1 0 row 1 1 0 end table close square brackets space space space space space space space space space space space space space space space space space equals open square brackets table row cell negative 1 plus 0 plus 0 end cell cell negative 2 plus 1 plus 0 end cell cell negative 3 plus 0 plus 0 end cell row cell 0 plus 0 plus 1 end cell cell 0 minus 1 plus 1 end cell cell 0 plus 0 plus 0 end cell row cell 2 plus 0 plus 4 end cell cell 4 plus 3 plus 4 end cell cell 6 plus 0 plus 0 end cell end table close square brackets space open square brackets table row cell negative 1 end cell cell negative 1 end cell cell negative 3 end cell row 1 0 0 row 6 11 6 end table close square brackets therefore space space space open square brackets table row cell negative 1 end cell 1 0 row 0 cell negative 1 end cell 1 row 2 3 4 end table close square brackets space open square brackets table row 1 2 3 row 0 1 0 row 1 1 0 end table close square brackets space equals open square brackets table row cell negative 1 end cell cell negative 1 end cell 3 row 0 0 0 row 2 11 6 end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space From space left parenthesis 1 right parenthesis space and space left parenthesis 2 right parenthesis space comma space we space get comma open square brackets table row 1 2 3 row 0 1 0 row 1 1 0 end table close square brackets space open square brackets table row cell negative 1 end cell 1 0 row 0 cell negative 1 end cell 1 row 2 3 4 end table close square brackets space not equal to space open square brackets table row cell negative 1 end cell 1 0 row 0 cell negative 1 end cell 1 row 2 3 4 end table close square brackets space open square brackets table row 1 2 3 row 0 1 0 row 1 1 0 end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space

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